The Paris Paint Company is in the process of planning labor force requirements and production levels for the next four quarters. The marketing department has provided production with the following forecasts of demand for Paris Paint over the next year:

Quarter	Demand Forecast (in thousands of gallons)
1	380
2	630
3	220
4	160

Assume that there are currently 280 employees with the company. Employees are hired for at least one full quarter. Hiring costs amount to $1,200 per employee and firing costs are $2,500 per employee. Inventory costs are $1 per gallon per quarter. Its is estimated that one worker produces 1,000 gallons of paint each quarter.

Assume that Paris currently has 80,000 gallons of paint in inventory and would like to end the year with an inventory of at least 20,000 gallons.

a)Formulate this as a linear program. Assume that stock-outs are allowed.

b) Solve the linear program. Round the variables and determine the cost of the resulting plan.